Recovery of crashed laptop hard drive - Am I doing this right?

I have a crashed Dell Inspiron 6000 laptop running (or rather, not running)
Windows XP Media Center Edition 2005.

To recover the data on the hard drive, I plan to buy an external hard drive
case with a USB plug that I will connect to my other laptop that is
functioning normally (HP Pavilion running Vista).

I will then use a free data recovery program, such as from acronis.com or
pcinspector.de, to pull the data off the hard drive.

Then I will return the hard drive to the Dell and reinstall Windows XP using
the setup cd.

Do you think this will work? Is there anything I need to take into
consideration?

Also, if you know of another data recovery program that you've had success
with, I would welcome your suggestion.

Thanks!